ASYMPTOTIC DISTRIBUTION-FREE TESTS FOR SEMIPARAMETRIC REGRESSIONS WITH DEPENDENT DATA

作者：Escanciano Juan Carlos^*; Carlos Pardo Fernandez Juan; Van Keilegom Ingrid

来源：Annals of Statistics, 2018, 46(3): 1167-1196.

DOI：10.1214/17-AOS1581

• Beta-mixing
• error distribution
• goodness-of-fit tests
• local polynomial estimation
• nonparametric regression

This article proposes a new general methodology for constructing nonparametric and semiparametric Asymptotically Distribution-Free (ADF) tests for semiparametric hypotheses in regression models for possibly dependent data coming from a strictly stationary process. Classical tests based on the difference between the estimated distributions of the restricted and unrestricted regression errors are not ADF. In this article, we introduce a novel transformation of this difference that leads to ADF tests with well-known critical values. The general methodology is illustrated with applications to testing for parametric models against nonparametric or semiparametric alternatives, and semiparametric constrained mean-variance models. Several Monte Carlo studies and an empirical application show that the finite sample performance of the proposed tests is satisfactory in moderate sample sizes.

• 出版日期2018-6